Post on 31-Mar-2020
Growth and the World Distribution of Income
By Xavier Sala-i-Martin
GDP Per Capita Since 1970World GDP Per Capita
$0
$1,000
$2,000
$3,000
$4,000
$5,000
$6,000
$7,000
$8,000
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
β-Divergencegr
owth
ypc70l5.8041 9.93357
-.027063
.05886
-DivergenceFigure 2. Variance of Log- Per Capita Income: 125 Countries
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
Variance of Log Per Capita Income Across Countries
Distribution: Individuals
Histogram Income Per Capita (countries)Fr
actio
n
ypc70331.656 5000 10000 1500020000
0
.1
.2
.3
Histogram: Population Weighted WDI (1970)Fr
actio
n
ypc70331.656 5000 10000 1500020000
0
.1
.2
.3
.4
.5
Histogram: Population Weighted WDI (2000)Fr
actio
n
ypc2000481.873 20000 40000
0
.1
.2
.3
.4
.5
.6
Aggregate Numbers do not show Personal Situation: Need
Individual Income Distribution• Problem: we do not have each person’s
income• We have
– (A) Per Capita GDP (PPP adjusted)– (B) Income Shares for some years
• We can combine these two data sources to estimate the WORLD DISTRIBUTION OF INCOME
Method
• Use micro surveys to anchor the dispersion• Use GDP Per Capita to anchor de MEAN of
the distribution.– This is subject to CONTROVERSY.
Again: Parametric or Non-Parametric?
• To estimate individual country distributions, we can:
• (A) Assume a functional form (say lognormal), use the variance from surveys and the mean from NA (or from surveys) and estimate the distribution– Bhalla (2002) “smooths out” the Lorenz curve using an
underlying two-parameter distribution– Quah (2002) estimates distribution for India and China
for 1988 and 1998 assuming the distributions are log-normal
Kernels• (B) Estimate non-parametric kernels• Which one is better? I will do both (you will see
that the results are quite similar)• Bandwidth =w=0.9*sd*(n-1/5), where sd is the
standard deviation of (log) income and n is the number of observations
• I also used Silverman’s optimal bandwidth• I did allow for a different bandwidth for every
country and year and I also forced all to have the same bandwidth. Results largely the same.
Start with a Histogram
Figure. 2a. Income Distribution: China
0
20000
40000
60000
80000
100000
5 6 6 7 7 8 9 9
Series1
ChinaChina
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970
China
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980
China
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990
China
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
IndiaIndia
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
USAUSA
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
USA (corrected scale)USA
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
$1,000 $10,000 $100,000 $1,000,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
IndonesiaIndonesia
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
BrazilBrasil
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
JapanJapan
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
Mexico
Mexico
0
1,000
2,000
3,000
4,000
5,000
6,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
NigeriaNigeria
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
Nigeria (corrected scale)Nigeria
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
$10 $100 $1,000 $10,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
The Collapse of the Soviet UnionUSSR-FSU
0
5,000
10,000
15,000
20,000
25,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970
USSR-FSU
0
5,000
10,000
15,000
20,000
25,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980
USSR-FSU
0
5,000
10,000
15,000
20,000
25,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1989
USSR-FSU
0
5,000
10,000
15,000
20,000
25,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 1989
USSR-FSU
0
5,000
10,000
15,000
20,000
25,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 2000 1989
USSR and FSUFigure 1g: Distribution of Income in USSR-FSU
0
5,000
10,000
15,000
20,000
25,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1989 1990 2000
World Distribution 1970Figure 2a: The WDI and Individual Country Distributions in 1970
0
40,000
80,000
120,000
160,000
200,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
Individual Countries World
World
China
India
USSR Japan USA
$1/day
World Distribution 2000Figure 2b: The WDI and Individual Country Distributions in 2000
0
40,000
80,000
120,000
160,000
200,000
240,000
280,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
Individual Countries World
World
China
India
FSU Nigeria USA Japan
$1/day
World Distribution Over TimeWDI-Various Years
0
50,000
100,000
150,000
200,000
250,000
300,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970
WDI-Various Years
0
50,000
100,000
150,000
200,000
250,000
300,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980
WDI-Various Years
0
50,000
100,000
150,000
200,000
250,000
300,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990
WDI-Various Years
0
50,000
100,000
150,000
200,000
250,000
300,000
$100 $1,000 $10,000 $100,000
thou
sand
s of
peo
ple
1970 1980 1990 2000
Poverty
Poverty RatesPoverty Rates
0%
5%
10%
15%
20%
25%
30%
35%
40%
1970 1975 1980 1985 1990 1995 2000
570$ 826$ 495$
Cumulative Distribution FunctionFigure 4: Cumulative Distribution Functions (Various Years)
0
0.2
0.4
0.6
0.8
1
$100 $1,000 $10,000 $100,000
1970 1980 1980 2000
$570/year
$2000/year
$5000/year
20%
16%
10%7%
62%54%50%41%
78%
67%
73%75%
Poverty HeadcountsPoverty Counts
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1970 1975 1980 1985 1990 1995 2000
570$ 826$ 495$
Regional PovertyPoverty Rates ($570)
0%
10%
20%
30%
40%
50%
60%
1970 1975 1980 1985 1990 1995 2000
Africa Latin America East Asia South Asia Middel East and NA Eastern Europe and CA
Regional PovertyPoverty Counts ($570)
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
1970 1975 1980 1985 1990 1995 2000
Africa Latin America East Asia South Asia Middel East and NA Eastern Europe and CA
Inequality
• UNDP 1999 Methodology:– Step 1: Show that Inequality within countries has been
increasing (cite USA, China, Latin America, etc.) – Step 2: Show Per Capita Income Across countries has
been diverging (so cross-country inequality has been increasing and cite Pritchett’s (1997) “Divergence Big Time” –you could also cite Barro and Sala-i-Martin (1992) or (1994).)
– Conclude: THEREFORE, global income inequality has been increasing!!!
• Right?
Wrong!
• Step 1: refers to citizens• Step 2: refers to countries• Steps 1 and 2 cannot be “added up” to come up
with global income inequality!• The concept of “cross country” inequality
should be “inequality that would exist in the world if all citizens within each country had same level of income, but different per capita incomes across countries”. The difference? POPULATION SIZES!
Recall β-convergencegr
owth
ypc70l5.8041 9.93357
-.027063
.05886
Population-Weighted β-convergence
grow
th
ypc70l6 7 8 9 10
-.03
-.02
-.01
0
.01
.02
.03
.04
.05
.06
.07
Gini
Gini
0.63
0.635
0.64
0.645
0.65
0.655
0.66
0.665
1970 1975 1980 1985 1990 1995 2000
Figure 7. Bourguignon-Morrisson and Sala-i-Martin: Global and Across-Country Gini
0.4
0.45
0.5
0.55
0.6
0.65
0.7
1820 1850 1880 1910 1940 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997
Bourguignon-Morrisson Sala-i-Martin Global Sala-i-Martin Across
Gini
Variance of Log IncomeVariance of Log Income
1.5
1.52
1.54
1.56
1.58
1.6
1.62
1.64
1.66
1.68
1970 1975 1980 1985 1990 1995 2000
Atkinson (0.5)
Atkinson with coefficient 0.5
0.33
0.335
0.34
0.345
0.35
0.355
0.36
0.365
1970 1975 1980 1985 1990 1995 2000
Atkinson (1)Atkinson with Coefficient 1
0.55
0.555
0.56
0.565
0.57
0.575
0.58
0.585
0.59
0.595
1970 1975 1980 1985 1990 1995 2000
Mean Log DeviationMean Logarithmic Deviation
0.8
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.9
0.91
1970 1975 1980 1985 1990 1995 2000
Theil IndexTheil
0.77
0.78
0.79
0.8
0.81
0.82
0.83
0.84
0.85
1970 1975 1980 1985 1990 1995 2000
Ratio Top 20% to Bottom 20%Figure 7e: World Income Inequality: Ratio Top 20% / Bottom 20%
7
8
9
10
11
12
1970 1975 1980 1985 1990 1995 2000
Ratio Top 10% to Bottom 10%Figure 7f: World Income Inequality: Ratio Top 10%/ Bottom 10%
20
22
24
26
28
30
32
1970 1975 1980 1985 1990 1995 2000
Decomposition
• Global Inequality = Inequality Across Countries + Inequality Within Countries
• Not all measures can be “decomposed” in the sense that the within and the across-country component add up to the global index of inequality
• Only the “Generalized Entropy” indexes can be decomposed: MLD and Theil
Mean Logarithmic Deviation
Global, 0.90
Global, 0.82
Across, 0.64
Across, 0.50
Within, 0.25Within, 0.32
0.0
0.2
0.4
0.6
0.8
1.0
1970 2000
Theil Index
Global, 0.84Global, 0.78
Across, 0.58
Across, 0.50
Within, 0.26 Within, 0.28
0.0
0.2
0.4
0.6
0.8
1.0
1970 2000
Lessons
• Across-Country inequalities decline• Within-Country inequalities increase, but not
enough to offset the decline in across-country inequalities so that overall inequality actually falls
• Across-Country inequalities are much larger: if you want to reduce inequalities across citizens, promote AGGREGATE growth in poor countries!
Inequalities have fallen…
Because Asia has been catching up withOECD.
If Africa does not start growing soon, inequalities will start increasing again...
Projected Inequalities if Africa does not Grow…
Global Projections if Same Growth as 1980-2000
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014 2018 2022 2026 2030 2034 2038 2042 2046 2050
Theil MLD
Conclusions
• Poverty: key determinant is GROWTH• Inequality: key determinant is GROWTH